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Smart-card based password authentication has been the most widely used two-factor authentication (2FA) mechanism for security-critical applications (e.g., e-Health, smart grid and e-Commerce) in the past decades, and it is likely to hold its status in the foreseeable future. Hundreds of this type of 2FA schemes have been proposed, yet to our knowledge, most of them are built on the intractability of conventional hard problems (e.g., discrete logarithm problems and integer factoring problems) which are no longer hard in the quantum era. With the recent advancements in quantum computing, the design of secure and efficient smart-card based password authentication schemes against quantum attacks is becoming increasingly urgent. However, it is not as simple as it seems, how to design such a quantum-resistant 2FA scheme is challenging due to the demanding security requirements and the resource-constrained …